Animating vertices from coordinates in "frame" files
Here is what I did (based upon the answer here):

import bpy #Blender Python
import bmesh #Blender mesh creation pkg
import glob

#function def:
def fileNameToData(filepath):
     #import first data file:
     file = open(filepath,'r')
     lines = file.readlines()
     data=[]
     for i in lines:
         data.append(list(map(float,i.split()[1:4])))
     return data

#number of objects / vertices
n = len(fileNameToData("000.txt")) # (000.txt is the first frame.)

#Read in all data files.
files = glob.glob('*.txt')
files.sort()
data = [] #data is of the format ((frame 1 verts: (2,3,3), (3,6,2), …), (frame 2 verts: (0,5,2), (3,3,5), …), …)
for f in files:
    data.append(fileNameToData(f))

n_frames = len(files)
bpy.context.scene.frame_end = n_frames

#add mesh object:
bpy.ops.mesh.primitive_circle_add(vertices=n)
obj = bpy.context.active_object

for i_frame in range(n_frames):
    block = obj.shape_key_add(name=str(i_frame), from_mix=False)  # returns a key_blocks member
    block.value = 1.0
    block.mute = True
    vertex_idx = 0
    for (vert, co) in zip(block.data, data[i_frame]):
        vert.co = co
    block.mute = True
    block.keyframe_insert(data_path='mute', frame=0, index=-1)
    block.mute = False
    block.keyframe_insert(data_path='mute', frame=i_frame + 1, index=-1)
    block.mute = True
    block.keyframe_insert(data_path='mute', frame=i_frame + 2, index=-1)